#ifndef GRID_MATH_TRACE_H
#define GRID_MATH_TRACE_H
namespace Grid {
//////////////////////////////////////////////////////////////////
// Traces: both all indices and a specific index 
/////////////////////////////////////////////////////////////////

inline ComplexF trace( const ComplexF &arg){    return arg;}
inline ComplexD trace( const ComplexD &arg){    return arg;}
inline RealF trace( const RealF &arg){    return arg;}
inline RealD trace( const RealD &arg){    return arg;}

template<int Level> inline ComplexF traceIndex(const ComplexF arg) { return arg;}
template<int Level> inline ComplexD traceIndex(const ComplexD arg) { return arg;}
template<int Level> inline RealF traceIndex(const RealF arg) { return arg;}
template<int Level> inline RealD traceIndex(const RealD arg) { return arg;}

template<class vtype,int N>
inline auto trace(const iMatrix<vtype,N> &arg) -> iScalar<decltype(trace(arg._internal[0][0]))>
{
    iScalar<decltype( trace(arg._internal[0][0] )) > ret;
    zeroit(ret._internal);
    for(int i=0;i<N;i++){
        ret._internal=ret._internal+trace(arg._internal[i][i]);
    }
    return ret;
}
template<class vtype>
inline auto trace(const iScalar<vtype> &arg) -> iScalar<decltype(trace(arg._internal))>
{
    iScalar<decltype(trace(arg._internal))> ret;
    ret._internal=trace(arg._internal);
    return ret;
}
////////////////////////////////////////////////////////////////////////////////////////////////////////
// Trace Specific indices.
////////////////////////////////////////////////////////////////////////////////////////////////////////
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline auto 
traceIndex (const iScalar<vtype> &arg) -> iScalar<decltype(traceIndex<Level>(arg._internal))>
{
  iScalar<decltype(traceIndex<Level>(arg._internal))> ret;
  ret._internal=traceIndex<Level>(arg._internal);
  return ret;
}
template<int Level,class vtype,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline auto
traceIndex (const iScalar<vtype> &arg) -> iScalar<vtype>
{
  return arg;
}

// If we hit the right index, return scalar and trace it with no further recursion
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel == Level >::type * =nullptr> inline 
auto traceIndex(const iMatrix<vtype,N> &arg) ->  iScalar<vtype> 
{
  iScalar<vtype> ret;
  zeroit(ret._internal);
  for(int i=0;i<N;i++){
    ret._internal = ret._internal + arg._internal[i][i];
  }
  return ret;
}

// not this level, so recurse
template<int Level,class vtype,int N,typename std::enable_if< iScalar<vtype>::TensorLevel != Level >::type * =nullptr> inline 
auto traceIndex(const iMatrix<vtype,N> &arg) ->  iMatrix<decltype(traceIndex<Level>(arg._internal[0][0])),N> 
{
  iMatrix<decltype(traceIndex<Level>(arg._internal[0][0])),N> ret;
  for(int i=0;i<N;i++){
  for(int j=0;j<N;j++){
    ret._internal[i][j] = traceIndex<Level>(arg._internal[i][j]);
  }}
  return ret;
}

// Allow to recurse if vector, but never terminate on a vector
// trace of a different index can distribute across the vector index in a replicated way
// but we do not trace a vector index.
 template<int Level,class vtype,int N,typename std::enable_if< iVector<vtype, N>::TensorLevel != Level >::type * =nullptr> inline 
auto traceIndex(const iVector<vtype,N> &arg) ->  iVector<decltype(traceIndex<Level>(arg._internal[0])),N> 
{
  iVector<decltype(traceIndex<Level>(arg._internal[0])),N> ret;
  for(int i=0;i<N;i++){
    ret._internal[i] = traceIndex<Level>(arg._internal[i]);
  }
  return ret;
}

}
#endif